Longitud de la diagonal del octágono

Dado que aquí hay un octágono regular de longitud de lado a , la tarea es encontrar la longitud de su diagonal.
Ejemplos: 
 

Input: a = 4
Output: 10.4525

Input: a = 5
Output: 13.0656

Enfoque : Del diagrama está claro que,
 

AB ^ 2 + BC ^ 2 = AC ^ 2 
aquí, en el triángulo AED, 
b ^ 2 + b ^ 2 = a ^ 2 
o, b = a / √ 2 ( consulte ) 
Entonces, AB = a + 2b = a + √2a 
y, BC = a 
Entonces, diagonal AC = a√(4 + 2√2)

A continuación se muestra la implementación del enfoque anterior: 
 

// C++ Program to find the diagonal
// of the octagon
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the diagonal
// of the octagon
float octadiagonal(float a)
{
 
    // side cannot be negative
    if (a < 0)
        return -1;
 
    // diagonal of the octagon
    return a * sqrt(4 + (2 * sqrt(2)));
}
 
// Driver code
int main()
{
    float a = 4;
    cout << octadiagonal(a) << endl;
 
    return 0;
}

// Java  Program to find the diagonal
// of the octagon
import java.util.*;
class solution
{
   
// Function to find the diagonal
// of the octagon
static double octadiagonal(double a)
{
   
    // side cannot be negative
    if (a < 0)
        return -1;
   
    // diagonal of the octagon
    return a * Math.sqrt(4 + (2 * Math.sqrt(2)));
}
   
// Driver code
public static void main(String args[])
{
    double a = 4;
    System.out.println( octadiagonal(a));
   
}
}
//contributed by Arnab Kundu

# Python3 Program to find the diagonal
# of the octagon
import math
# Function to find the diagonal
# of the octagon
def octadiagonal(a):
 
    # side cannot be negative
    if (a < 0):
        return -1;
 
    # diagonal of the octagon
    return a * math.sqrt(4 + (2 * math.sqrt(2)))
 
 
# Driver code
if __name__=='__main__':
    a = 4
    print (octadiagonal(a))
 
# This code is contributed by
# Shivi_Aggarwal

// C# Program to find the diagonal
// of the octagon
using System;
 
class GFG
{
 
// Function to find the diagonal
// of the octagon
static double octadiagonal(double a)
{
 
    // side cannot be negative
    if (a < 0)
        return -1;
 
    // diagonal of the octagon
    return a * Math.Sqrt(4 +
          (2 * Math.Sqrt(2)));
}
 
// Driver code
public static void Main()
{
    double a = 4;
    Console.WriteLine(octadiagonal(a));
}
}
 
// This code is contributed
// by inder_verma

<?php
// PHP program to find the diagonal
// of the octagon
 
// Function to find the diagonal
// of the octagon
function octadiagonal($a)
{
 
    // side cannot be negative
    if ($a < 0)
        return -1;
 
    // diagonal of the octagon
    return $a * sqrt(4 + (2 * sqrt(2)));
}
 
// Driver code
 
    $a = 4;
    echo octadiagonal($a) ;
 
// This code is contributed
// by inder_verma
 
?>

<script>
// javascript  Program to find the diagonal
// of the octagon
 
// Function to find the diagonal
// of the octagon
function octadiagonal(a)
{
   
    // side cannot be negative
    if (a < 0)
        return -1;
   
    // diagonal of the octagon
    return a * Math.sqrt(4 + (2 * Math.sqrt(2)));
}
 
var a = 4;
document.write( octadiagonal(a).toFixed(5));
 
// This code is contributed by 29AjayKumar
</script>

10.4525

Complejidad del tiempo: O(1)

Espacio Auxiliar: O(1)